Abstract

Optical quantum states based on entangled photons are the key resource in quantum-information science. The realization of multiplexed multiple entanglement are necessary for developing high-capacity quantum information process. Silicon-on-insulator (SOI) has recently become a leading platform for generating and processing of non-classical optical states. In this work, by combining the wavelength- and time-division multiplexing technologies, we demonstrate a multiplexing time-bin entangled photon pair source based on a silicon nanowire waveguide and distribute entangled photons into 3(time) × 14(wavelength) channels independently. The indistinguishability of photon pairs in each time channel is confirmed by a fourfold Hong-Ou-Mandal quantum interference. Our work paves a new and promising way to achieve a high capacity quantum communication and to generate a multiple-photon non-classical state.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Quantum communication can be used to transfer quantum information between remote users through the free space or optical fibers, therefore the channel capacity is one of the most important parameters describing the communication systems. In classical optical communication systems, in order to increase the channel capacity, multiple channels are used to handle the huge amounts of information needed to be transferred independently. For example, the wavelength-division multiplexing (WDM), in which signals separated in wavelength, is used to provide many channels to transfer signals parallel; or a time-division multiplexing (TDM) is used to handle the information in different time slots independently; even recently, a spatial-division multiplexing (SDM) has been used to further improve the channel capacity [1].

Entangled photon pairs play a major role in many quantum information fields [2–6], especially in quantum communications [2]. To realize a long-distance quantum communication, a quantum repeater [7] has to be used to overcome the problem of communication fidelity decreasing exponentially with the channel length, which requires the distribution of quantum entanglement between adjacent nodes firstly. So how to share larger amounts of entanglement in smaller periods of time is a key for achieving a high communication rate. One promising way is to use multiplexing of photon’s different degrees of freedoms to parallel handle the large amounts of information in multiple channels independently. Recently, significant efforts have been devoted in this field to, for example, generate multiplexed entangled photons by WDM [8,9] or create multiphoton entangled states [10,11] for high-capacity and high-speed quantum information processing. Although the combination of SDM and TDM of photons, individual TDM or WDM has been used to enhance the probability of single-photon output [12–14], however, simultaneously using TDM and WDM techniques to distribute entangled photon pairs has not been realized yet.

Usually, entangled photon pairs can be generated by using spontaneous parametric down-conversion (SPDC) [15,16] or spontaneous four-waving mixing (SFWM) [17,18] in nonlinear crystals or waveguides. Although various systems can be used to generate entanglement states, SOI is a very promising platform, as it offers high integrating density, a strong χ3 optical nonlinearity, mature fabrication techniques and compatibility with telecom techniques and complementary metal oxide semiconductor (CMOS) electronics [19–21]. Comparing with conventional fiber-based entangled photon-pair sources [17], SOI-based sources have much lower noise level in telecom C-band applications because of a much narrow Raman-scattering peak(105GHz) in single crystalline silicon(Si) [19,21]. Those features prove that SOI platform is suitable to develop integrated quantum photonics devices [19–23]. Furthermore, a single nanowire waveguide has a broad photon-pair emission spectrum, which is well suited for distribution over 100 GHz DWDM channels [18].

In this work, we report in the following an experimental realization of a simultaneous time and frequency multiplexing of time-bin entangled source [24,25] in a silicon nanowire waveguide (SNW). Firstly, we use temporal-multiplexed pulses to pump a SNW to generate a time-bin entangled photon pair with a broad spectrum, then we de-multiplex them in time domain by optical switches and in frequency domain by DWDM components, and distribute entangled photons into 3(time) × 14(wavelength) channels independently. In this way, we can increase the bit rate by a factor 42 compared with the single channel systems if it is applied in quantum communications. Furthermore, the entanglement states belonging to different time channel can be adjusted independently due to the unique design of our scheme. We experimentally show nearly noise-free two-photon interferences with high visibilities in 3(time) × 5 (wavelength) channels, clearly demonstrating the time-energy entanglement in each pair and the independence of three time channels. Finally, we perform a four-fold Hong-Ou-Mandel (HOM) [26] interference between photon pairs from different time slots to demonstrate the indistinguishability of photons at different time slots. Such a strategy enables the increase of dimensions of multiple entanglements modes, reveals the potential to offer a new and promising way to achieve high bit rate in quantum communication and to generate a multiple and customizable non-classical state.

2. Time- and wavelength-division multiplexing and de-multiplexing scheme

The principle diagram of our scheme is illustrated in Fig. 1. In the TWDM scheme, the original pulsed pump has a period of NT. Using two 1-to-N couplers and optical delay line with a delay of 0, T… NT, the period of the pump pulse becomes T and the repetition rate R is increased by N times. We defined the pulse in each time slots as time division channels. Then, a SNW is pumped by multiplexed pulses, so temporal multiplexed entangled photon pairs with a broad spectrum can be generated in N time slots (T1, T2 ... Tn). Entanglement can be established between photons in their different degrees of freedoms. And we can control the phase of entanglement states in different time channel independently by adjusting the phase of corresponding pumped pulse. In other words, entanglement states belonging to different time channels differs from each other. Comparing to the traditional multiplexing entanglement source, this is a great advantage of our temporal multiplexed scheme.

 

Fig. 1 The principle diagram for entanglement source. Multiplexed pulses pump an SNW to generate entangled photon pairs in N time slots. The entangled photon pairs are firstly split into temporal channels using a time division multiplexer (TDM), which is consist of optical switches. Then, the entangled photon pairs are distributed to multiusers by DWDM.

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For the procedure of de-multiplexing, we use an electronic circuit to extract timing information from the pump pulse. The synchronous clock is subsequently used to control optical switches which can actively route entangled photon pairs into N time slots. By merging wavelength-division multiplexing/de-multiplexing (DWDM) technique, the entangled photon pairs in each time slot are shared by M pairs of users. Thus, the entangled modes can be increased to N (time) × M (wavelength), offering great promising for high-capacity quantum communication systems.

3. Multiplexed time-bin entangled source

Figure 2 showed the entire experimental setup for producing and analyzing multiple frequency-mode time-bin entanglement. The nonlinear device employed in our experiment is a SNW with a length of 1cm and transverse dimensions of 220nm (height) × 450nm (width). The weak and anomalous dispersion of SNW enables broadband phase matching for SFWM, generating photon pairs over a broad bandwidth. Such a bandwidth would allow entanglement distribution up to 30 standard channel pairs using high performance multi-channel DWDM. The external pump laser is coupled to the waveguide through input-coupling gratings. And the total insertion losses from input to output port is about 10 dB, the whole loss of the system is shown in section 6.

 

Fig. 2 Experimental setup for multiplexed time-bin entanglement source. TA, tunable attenuator; PC, fiber polarization controller; UMI, unbalanced Michelson fiber interferometer; DDG1, DDG2, digital delay generator; FRM, Faraday rotation mirror; SSPD1 and SSPD2, superconducting single-photon detector; TIA, time interval analyzer. ODL, optical delay line.

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The pump laser is a mode-locked fiber laser with a repetition rate of 27.97MHz (35ns period) and a pulse duration 15ps. Each pulse is split into three pulses spaced by 10ns using two one-to-three fiber couplers and three optical fiber delay lines. We obtained time-division multiplexed time-bin entanglements by passing three pulses through three stabilized unbalanced Michelson fiber interferometers (UMI, 1.6ns time difference between two interfering beams) [17]. Each UMI is individually sealed in a copper box and thermally insulated from the air. The temperature of each copper box is controlled with a homemade semiconductor Peltier temperature controller with temperature fluctuations of ± 2 mK.

Now we give a brief theoretical description of our time-division multiplexed time-bin entanglements. After each pulse in different channel is divided into two time bins by UMI, the pump photon is prepared in state:

|ψp1=12(|Seiϕp1|L)
|ψp2=12(|Seiϕp2|L)
|ψp3=12(|Seiϕp3|L)
where S and L signify the short and long arms of interferometer through which photon passes, respectively, and ϕp1,ϕp2,ϕp3 is the phase difference between two interfering beams in each UMI, which means the phase of entanglement states in each time channel can be adjusted independently. After the SNW, the entangled states in different time slots can be expressed as:

|ΦT1=12(|SSei2ϕP1|LL)
|ΦT2=12(|SSei2ϕP2|LL)
|ΦT3=12(|SSei2ϕP3|LL)

A temporal de-multiplexing setup is consist of two active 1 × 2 optical switches and electronics synchronization control module. The setup is used to route the multiplexed time-bin entanglements to each quantum branch channels (see Fig. 2). The 1 × 2 optical switch is a high-speed electro-optic polarization-independent switch, made from a lithium Niobate single mode waveguide. The switching network is driven by the synchronous clock signals which is obtained from the pump laser.

The output from optical switch network is connected to 32 × 100 GHz bandwidth DWDM. Here, photons pairs generated in SNW are time-bin entangled. Conservation of the energy implies that the entangled photons are always produced symmetrically with respect to the center emission spectrum. Moreover, the spectrum of the photon is broad enough to cover the entire telecom C-band, thus. And the DWDM is well suited for de-multiplexing the entangled states. The corresponding channels of DWDM at equal shifts from the pump frequency are correlated. We relabel signal and idler photons S1-S14 and I1-I14 and a detail definition of the central wavelength of the international telecommunications union (ITU) grid is shown in Table 1 in section 6. In the experiment, we fix the pump wavelength at 1550.12nm (ITU channel 31) and choose five channel pairs to experimentally characterize the quality of entanglement.

Tables Icon

Table 1. Definition of the wavelengths of the standard ITU grids for the signal and idler photons

The signal and idler photons passed through two UMIs individually with an imbalance (1.5 ns) identical to that used for the pump laser. This setup allowed the measurement of the quantum interference between the signal and idler photons. To characterize the time- and wavelength-division multiplexing entanglement of the source, we selected 15 channel pairs in different time slot and different wavelength and obtained quantum interference with high raw visibilities above 90% (see Fig. 3(a).) After subtracting the background noise, the visibility was found to be above 95% in all channel pairs. If the visibility of the two-photon interference is >70.7%, the Clauster-Horne-Shimony-Holt (CHSH) inequality would be violated [27], proving the entanglement between photons. Our results clearly demonstrated the entanglement between photon pairs from all channels.

 

Fig. 3 Quality characterizations of time-and wavelength-division multiplexed entanglement source. (a). Raw visibilities of two-photon interference for 3 × 5 channel pairs. (b). Two-photon coincidence in 60s for channel S8-I8-T1 when the idler and the pump UMI phase is fixed at π/2 (solid blue line) and the idler and the signal UMI phases are fixed at π/2 (solid blue line) in channel. (c). Two-photon coincidence in 300s for channel S8-I8-T2 when the idler and the pump UMI phases are fixed at 0 (solid blue line) and the idler and the signal UMI phases are fixed at 0 (solid blue line). (d). Two-photon coincidence in 300s for channel S8-I8-T3 when the idler and the pump UMI phases are fixed at π/2 (solid blue line) and the idler and the signal UMI phases are fixed at π/2(solid blue line).

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To further characterize quantum states in different temporal slots, we measure the two-photon interference fringes between two photons from three channels. When SFWM process (as in this work) in nonlinear media is used to generate entangled photon pairs, quantum interference is expected to be proportional to 1Vcos(2ϕpϕsϕi), where ϕs and ϕi are the relative phases of the UMIs in the signal and idler ports, respectively. We obtained three groups of interference fringes (see. Figures 3(b)-(d)) by adjusting the independent UMIs in different time channels. As shown in Figs. 3(b)-(d) with dashed and solid lines, the two-photon interference fringes have a period of oscillation of π for the pump phase and 2π for the signal (idler) phase, which confirm the phase dependency in SFWM. To verify the independence of three time channels, we fixed the pump UMI phase in T1 and T2 channel at π/2 and T3 channel 0 at the same time. As shown in Figs. 3(b)-(d), the phase of interference fringes in different time channel is independent changing as expect. The distinct properties of our temporal multiplexing and de-multiplexing system have enormous potential applications in the future quantum communication.

4. Photon pairs indistinguishability check

To check indistinguishability of de-multiplexed photon pairs, we performed a four-fold HOM interference experiment (Fig. 4) between photon pairs generated in different time channel. We removed UMIs in the first experiment and chose two groups of channel pairs for experiment (see Fig. 5). The photons with the same wavelength, to be interfered, were chosen from different time channels. A tunable optical delay line was applied to output photons from different channels so that they can appear in a time slot. Then idler channels were input into a 50:50 fiber coupler whose two output ports were followed by SSPD1 and SSPD2. To ensure that the photons from the two idler channels had the same polarization, two PCs were installed before fiber coupler. The signal photons were received by SSPD3 and SSPD4 and set as trigger signals.

 

Fig. 4 Experimental setup for HOM interference between photon pairs at different time slots generated from the same SSW. TA, tunable attenuator; PC, fiber polarization controller; DDG1, DDG2, digital delay generator; SSPD1 and SSPD2, superconducting single-photon detector; TIA, time interval analyzer; OC, optical coupler. ODL, optical delay line. TODL, tunable optical delay line.

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Fig. 5 Four-fold HOM interference fringes. (a). The measured four-fold dip between S14-I14-T3 and S14-I14-T2 channel pairs. (b). The measured four-fold dip between S8-I8-T1 and S8-I8-T2 channel pairs.

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A higher pump powers is applied to have sufficient coincidence counts to make the statistics meaningful. With the increasing of pump power, multi-photon effect appears which reduces the visibility of the HOM dip. In the measurement, the pump power is set as 0.5mw under which coincidence to accidental coincidence ratio of 8 for both channel pairs were obtained. Figure 5 shows the obtained net four-fold coincidences as a function of optical delay. Without subtraction of any background counts, the raw visibility of the four-fold HOM dip between S14-I14-T3 and S14-I14-T2 channel pairs (S8-I8-T1 and S8-I8-T2 channel pairs) is 58.48 ± 15.02% (55.43 ± 3.93%), indicating that non-classical interference occurred between channel pairs in different temporal modes. The dark coincidence was measured by blocking one arm of the coupler, and summing the two results together. When subtracting the dark coincidence, we obtain net visibility of 92.9 ± 6.2% (76.9 ± 5.7%).

In this experiment, we use 100GHz DWDM (the equivalent bandwidth of Gaussian filter is 40 GHz, see Fig. 5) as spectral filter to limit the photon coherence time just like in the previous system [27]. The spectral purity of the heralded photons is an important factor that determined the visibility in the previous HOM experiment using a photon pair source based on bulk crystals [28]. Since we use the tight spectral filter, we consider this is not main reason for the visibility degradation. These are other possible reasons for the limitation of the visibility. The probable main reason of the visibility degradation is the large leakage of pump photon, which may have led to accidental coincidences caused by multiphoton emission events. The maximum visibility caused by multiphoton emission events is approximately given by [29]

V11+8μ1+12μ
where μ denotes the average photon-pair number per pulse. We look at the rate of (no-interfering) four-fold coincidence detection then we have

C4=Rμ2ηs2ηi2/2

where R is the laser repetition rate. ηs,ηi is the effective detection efficiencies which can be found in section 6.2. Four-fold coincidence rateC4 for two experiment is 50/1000s and 150/1000s. Then we have μ10.082(μ20.256) for each experiment, the maximum visibility is calculated to be V183%(V175%).

Another reason is that the timing jitter caused by the relatively broad pump pulse. When the pump pulse width is comparable to or broader than the coherence time of the photon pair, we observe the timing jitter of the generated photons, which results in the temporal distinguishability. In our experiment, the photon pair coherence time (11ps) is close to the pump pulse width (15ps). If the ratio between the pump pulse width and the photon pair coherence time is given by r the expect visibility of a HOM dip obtained with SFWM-based sources is expressed as [30]

V2=1+r21+r2/2

With the parameter values stated above, the visibility is calculated to be ~88%. The further visibility degradation of Fig. 5(b) stem from the different loss between S8-I8-T1 and S8-I8-T2 channels. The higher loss of S8-I8-T2 is generated by the additional optical switch (see Fig. 4). We believe that a combination of the above factors resulted in the HOM visibility of two experiments.

5. Conclusion and outlook

We have proposed and experimentally realized a scheme to generate a time- and wavelength-division multiplexed entangled source using a SNW, and simultaneously distributed photonic time-energy entangled photon pairs over 3 × 14 channels by combining DWDM and TDM techniques. The perfect visibilities of two-photon interference in all 3 × 5 channels clearly demonstrate the high entanglement in each channel pair. Furthermore, a four-fold HOM experiment between two photon pairs in different time slots have been reported, which demonstrates the indistinguishability between the photon pairs generated in different temporal mode. Generating photon pairs in different time slots enables an additional freedom, which makes multipartite entanglement readily available. Two-photon time-bin entangled qubits have been used successfully for linear universal quantum computation [4], and the parallel generation and processing of multiple qubits can directly enhance the information capacity. Our system’s capacity can straightforwardly be scaled up by using a denser channels spacing (e.g. current commercially available 12.5GHz or 25GHz multichannel ultra-DWDMs), relied on broadband phase matching condition engineering on a single-SOI-nanowire, as it has recently been reported in [9], and by using a higher speed and lower-loss switch for increasing temporal mode. In conclusion, this work provides a road map for creating high-capacity entanglement-based quantum communication system and for generating complex quantum states, which extends significantly the ability of integrated quantum photonics.

6 Appendix

6.1. Definition of the wavelengths of the standard ITU grids

The corresponding wavelengths for the correlated signal and idler photons are defined in Table 1. The bolded channels are used for characterizing the entanglement in the experiments. The pump wavelength is located at the center of channel C34.

6.2. Loss management

We would like to give an estimation of whole detection efficiencies for photon pairs in different channels. The insertion loss of the silicon waveguide is 5.00dB for both photons, the filtering loss of the cascade DWDM filters is about 2.00dB. The insertion loss of each path of electro-optic switch is 2.5dB. The insertion loss of UMI is 4.7dB. Taking into account the detection efficiency of the superconducting single-photon detector (70%, 1.5dB), the overall detection efficiency for signal photon and idler photon in T1 channel (pass through switches once) are 15.7dB and for signal photon and idler photon in T2 channel/T3 channel (pass through switches twice) are 18.2dB.

6.3. More data about the photon source

In the single-pass configuration, we measure the single count and coincidence to accidental coincidence ratio (CAR) for 15 correlated channel pairs, when the pump power is fixed at 0.3 mw. Results are showed in Fig. 6. The different single count rates between wavelength channels arise from the inhomogeneous SFWM gains, Raman scattering of the signal and idler bands and nonuniform losses of different DWDM channels. The different single count rates between T1 and T2/T3 time channels arise from the 3dB loss of additional switch. The CAR increases when the shift in the signal and idler wavelength increase. The peak value of CAR occurs in the S11-I11 channel.

 

Fig. 6 More data about the photon source. (a). single count rate for correlated channel pairs. (b). CARs for different correlated channel pairs from S14-I14-T1 to S2-I2-T3.

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Funding

National Natural Science Foundation of China (NSFC) (61435011, 61525504, 61605194, 61675188); the National Key Research and Development Program of China (2016YFA0302600); The Anhui initiative in Quantum information Technologies (AHY020200); the China Postdoctoral Science Foundation (2016M590570); and the Fundamental Research Funds for the Central Universities.

Acknowledgments

We would like to thank Dr. Xiao-Min Hu for lending us the multi-photon coincidence device and guiding us in using the device during the experiment.

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References

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  1. J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
    [Crossref]
  2. H. J. Kimble, “The quantum internet,” Nature 453(7198), 1023–1030 (2008).
    [Crossref] [PubMed]
  3. D. Deutsch, “Quantum-Theory, the Church-Turing Principle and the Universal Quantum Computer,” Proc. R. Soc. A Math. Phys. Eng. Sci.400, 97–117 (1985).
    [Crossref]
  4. P. C. Humphreys, B. J. Metcalf, J. B. Spring, M. Moore, X. M. Jin, M. Barbieri, W. S. Kolthammer, and I. A. Walmsley, “Linear Optical Quantum Computing in a Single Spatial Mode,” Phys. Rev. Lett. 111(15), 150501 (2013).
    [Crossref] [PubMed]
  5. M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429(6988), 161–164 (2004).
    [Crossref] [PubMed]
  6. Z. Y. Zhou, S. L. Liu, Y. Li, D. S. Ding, W. Zhang, S. Shi, M. X. Dong, B. S. Shi, and G. C. Guo, “Orbital Angular Momentum-Entanglement Frequency Transducer,” Phys. Rev. Lett. 117(10), 103601 (2016).
    [Crossref] [PubMed]
  7. H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, “Quantum repeaters: The role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81(26), 5932–5935 (1998).
    [Crossref]
  8. D. Aktas, B. Fedrici, F. Kaiser, T. Lunghi, L. Labonte, and S. Tanzilli, “Entanglement distribution over 150 km in wavelength division multiplexed channels for quantum cryptography,” Laser Photonics Rev. 10(3), 451–457 (2016).
    [Crossref]
  9. F. Kaiser, D. Aktas, B. Fedrici, T. Lunghi, L. Labonte, and S. Tanzilli, “Optimal analysis of ultra broadband energy-time entanglement for high bit-rate dense wavelength division multiplexed quantum networks,” Appl. Phys. Lett. 108(23), 231108 (2016).
    [Crossref]
  10. C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351(6278), 1176–1180 (2016).
    [Crossref] [PubMed]
  11. M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546(7660), 622–626 (2017).
    [Crossref] [PubMed]
  12. G. J. Mendoza, R. Santagati, J. Munns, E. Hemsley, M. Piekarek, E. Martin-Lopez, G. D. Marshall, D. Bonneau, M. G. Thompson, and J. L. O’Brien, “Active temporal and spatial multiplexing of photons,” Optica 3(2), 127–132 (2016).
    [Crossref]
  13. C. Xiong, X. Zhang, Z. Liu, M. J. Collins, A. Mahendra, L. G. Helt, M. J. Steel, D. Y. Choi, C. J. Chae, P. H. W. Leong, and B. J. Eggleton, “Active temporal multiplexing of indistinguishable heralded single photons,” Nat. Commun. 7, 10853 (2016).
    [Crossref] [PubMed]
  14. X. Zhang, I. Jizan, J. He, A. S. Clark, D. Y. Choi, C. J. Chae, B. J. Eggleton, and C. Xiong, “Enhancing the heralded single-photon rate from a silicon nanowire by time and wavelength division multiplexing pump pulses,” Opt. Lett. 40(11), 2489–2492 (2015).
    [Crossref] [PubMed]
  15. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75(24), 4337–4341 (1995).
    [Crossref] [PubMed]
  16. Y. Li, Z. Y. Zhou, D. S. Ding, and B. S. Shi, “CW-pumped telecom band polarization entangled photon pair generation in a Sagnac interferometer,” Opt. Express 23(22), 28792–28800 (2015).
    [Crossref] [PubMed]
  17. Y. H. Li, Z. Y. Zhou, Z. H. Xu, L. X. Xu, B. S. Shi, and G. C. Guo, “Multiplexed entangled photon-pair sources for all-fiber quantum networks,” Phys. Rev. A 94(4), 043810 (2016).
    [Crossref]
  18. Y. H. Li, Z. Y. Zhou, L. T. Feng, W. T. Fang, S. L. Liu, S. K. Liu, K. Wang, X. F. Ren, D. S. Ding, L. X. Xu, and B. S. Shi, “On-Chip Multiplexed Multiple Entanglement Sources in a Single Silicon Nanowire,” Phys. Rev. Appl. 7(6), 064005 (2017).
    [Crossref]
  19. F. Mazeas, M. Traetta, M. Bentivegna, F. Kaiser, D. Aktas, W. Zhang, C. Ramos, L. Ngah, T. Lunghi, E. Picholle, N. Belabas-Plougonven, X. Le Roux, É. Cassan, D. Marris-Morini, L. Vivien, G. Sauder, L. Labonté, and S. Tanzilli, “High-quality photonic entanglement for wavelength-multiplexed quantum communication based on a silicon chip,” Opt. Express 24(25), 28731–28738 (2016).
    [Crossref] [PubMed]
  20. J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, V. Zwiller, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8(2), 104–108 (2014).
    [Crossref]
  21. Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15(25), 16604–16644 (2007).
    [Crossref] [PubMed]
  22. J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3(6), 346–350 (2009).
    [Crossref]
  23. J. W. Silverstone, R. Santagati, D. Bonneau, M. J. Strain, M. Sorel, J. L. O’Brien, and M. G. Thompson, “Qubit entanglement between ring-resonator photon-pair sources on a silicon chip,” Nat. Commun. 6(1), 7948 (2015).
    [Crossref] [PubMed]
  24. W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Violation of bell inequalities by photons more than 10 km apart,” Phys. Rev. Lett. 81(17), 3563–3566 (1998).
    [Crossref]
  25. I. Marcikic, H. de Riedmatten, W. Tittel, H. Zbinden, M. Legré, and N. Gisin, “Distribution of time-bin entangled qubits over 50 km of optical fiber,” Phys. Rev. Lett. 93(18), 180502 (2004).
    [Crossref] [PubMed]
  26. C.-K. Hong, Z.-Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
    [Crossref] [PubMed]
  27. Z. Zhao, T. Yang, Y. A. Chen, A. N. Zhang, M. Zukowski, and J. W. Pan, “Experimental violation of local realism by four-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 91(18), 180401 (2003).
    [Crossref] [PubMed]
  28. P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, and I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum States,” Phys. Rev. Lett. 100(13), 133601 (2008).
    [Crossref] [PubMed]
  29. J. Fulconis, O. Alibart, W. J. Wadsworth, and J. G. Rarity, “Quantum interference with photon pairs using two micro-structured fibres,” New J. Phys. 9(8), 276 (2007).
    [Crossref]
  30. K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, “Indistinguishable photon pair generation using two independent silicon wire waveguides,” New J. Phys. 13(6), 065005 (2011).
    [Crossref]

2017 (2)

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546(7660), 622–626 (2017).
[Crossref] [PubMed]

Y. H. Li, Z. Y. Zhou, L. T. Feng, W. T. Fang, S. L. Liu, S. K. Liu, K. Wang, X. F. Ren, D. S. Ding, L. X. Xu, and B. S. Shi, “On-Chip Multiplexed Multiple Entanglement Sources in a Single Silicon Nanowire,” Phys. Rev. Appl. 7(6), 064005 (2017).
[Crossref]

2016 (8)

F. Mazeas, M. Traetta, M. Bentivegna, F. Kaiser, D. Aktas, W. Zhang, C. Ramos, L. Ngah, T. Lunghi, E. Picholle, N. Belabas-Plougonven, X. Le Roux, É. Cassan, D. Marris-Morini, L. Vivien, G. Sauder, L. Labonté, and S. Tanzilli, “High-quality photonic entanglement for wavelength-multiplexed quantum communication based on a silicon chip,” Opt. Express 24(25), 28731–28738 (2016).
[Crossref] [PubMed]

G. J. Mendoza, R. Santagati, J. Munns, E. Hemsley, M. Piekarek, E. Martin-Lopez, G. D. Marshall, D. Bonneau, M. G. Thompson, and J. L. O’Brien, “Active temporal and spatial multiplexing of photons,” Optica 3(2), 127–132 (2016).
[Crossref]

C. Xiong, X. Zhang, Z. Liu, M. J. Collins, A. Mahendra, L. G. Helt, M. J. Steel, D. Y. Choi, C. J. Chae, P. H. W. Leong, and B. J. Eggleton, “Active temporal multiplexing of indistinguishable heralded single photons,” Nat. Commun. 7, 10853 (2016).
[Crossref] [PubMed]

Z. Y. Zhou, S. L. Liu, Y. Li, D. S. Ding, W. Zhang, S. Shi, M. X. Dong, B. S. Shi, and G. C. Guo, “Orbital Angular Momentum-Entanglement Frequency Transducer,” Phys. Rev. Lett. 117(10), 103601 (2016).
[Crossref] [PubMed]

D. Aktas, B. Fedrici, F. Kaiser, T. Lunghi, L. Labonte, and S. Tanzilli, “Entanglement distribution over 150 km in wavelength division multiplexed channels for quantum cryptography,” Laser Photonics Rev. 10(3), 451–457 (2016).
[Crossref]

F. Kaiser, D. Aktas, B. Fedrici, T. Lunghi, L. Labonte, and S. Tanzilli, “Optimal analysis of ultra broadband energy-time entanglement for high bit-rate dense wavelength division multiplexed quantum networks,” Appl. Phys. Lett. 108(23), 231108 (2016).
[Crossref]

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351(6278), 1176–1180 (2016).
[Crossref] [PubMed]

Y. H. Li, Z. Y. Zhou, Z. H. Xu, L. X. Xu, B. S. Shi, and G. C. Guo, “Multiplexed entangled photon-pair sources for all-fiber quantum networks,” Phys. Rev. A 94(4), 043810 (2016).
[Crossref]

2015 (3)

2014 (1)

J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, V. Zwiller, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8(2), 104–108 (2014).
[Crossref]

2013 (1)

P. C. Humphreys, B. J. Metcalf, J. B. Spring, M. Moore, X. M. Jin, M. Barbieri, W. S. Kolthammer, and I. A. Walmsley, “Linear Optical Quantum Computing in a Single Spatial Mode,” Phys. Rev. Lett. 111(15), 150501 (2013).
[Crossref] [PubMed]

2012 (1)

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

2011 (1)

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, “Indistinguishable photon pair generation using two independent silicon wire waveguides,” New J. Phys. 13(6), 065005 (2011).
[Crossref]

2009 (1)

J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nat. Photonics 3(6), 346–350 (2009).
[Crossref]

2008 (2)

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, and I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum States,” Phys. Rev. Lett. 100(13), 133601 (2008).
[Crossref] [PubMed]

H. J. Kimble, “The quantum internet,” Nature 453(7198), 1023–1030 (2008).
[Crossref] [PubMed]

2007 (2)

Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15(25), 16604–16644 (2007).
[Crossref] [PubMed]

J. Fulconis, O. Alibart, W. J. Wadsworth, and J. G. Rarity, “Quantum interference with photon pairs using two micro-structured fibres,” New J. Phys. 9(8), 276 (2007).
[Crossref]

2004 (2)

I. Marcikic, H. de Riedmatten, W. Tittel, H. Zbinden, M. Legré, and N. Gisin, “Distribution of time-bin entangled qubits over 50 km of optical fiber,” Phys. Rev. Lett. 93(18), 180502 (2004).
[Crossref] [PubMed]

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, “Super-resolving phase measurements with a multiphoton entangled state,” Nature 429(6988), 161–164 (2004).
[Crossref] [PubMed]

2003 (1)

Z. Zhao, T. Yang, Y. A. Chen, A. N. Zhang, M. Zukowski, and J. W. Pan, “Experimental violation of local realism by four-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 91(18), 180401 (2003).
[Crossref] [PubMed]

1998 (2)

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Violation of bell inequalities by photons more than 10 km apart,” Phys. Rev. Lett. 81(17), 3563–3566 (1998).
[Crossref]

H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, “Quantum repeaters: The role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81(26), 5932–5935 (1998).
[Crossref]

1995 (1)

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75(24), 4337–4341 (1995).
[Crossref] [PubMed]

1987 (1)

C.-K. Hong, Z.-Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
[Crossref] [PubMed]

Agrawal, G. P.

Ahmed, N.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Aktas, D.

D. Aktas, B. Fedrici, F. Kaiser, T. Lunghi, L. Labonte, and S. Tanzilli, “Entanglement distribution over 150 km in wavelength division multiplexed channels for quantum cryptography,” Laser Photonics Rev. 10(3), 451–457 (2016).
[Crossref]

F. Kaiser, D. Aktas, B. Fedrici, T. Lunghi, L. Labonte, and S. Tanzilli, “Optimal analysis of ultra broadband energy-time entanglement for high bit-rate dense wavelength division multiplexed quantum networks,” Appl. Phys. Lett. 108(23), 231108 (2016).
[Crossref]

F. Mazeas, M. Traetta, M. Bentivegna, F. Kaiser, D. Aktas, W. Zhang, C. Ramos, L. Ngah, T. Lunghi, E. Picholle, N. Belabas-Plougonven, X. Le Roux, É. Cassan, D. Marris-Morini, L. Vivien, G. Sauder, L. Labonté, and S. Tanzilli, “High-quality photonic entanglement for wavelength-multiplexed quantum communication based on a silicon chip,” Opt. Express 24(25), 28731–28738 (2016).
[Crossref] [PubMed]

Alibart, O.

J. Fulconis, O. Alibart, W. J. Wadsworth, and J. G. Rarity, “Quantum interference with photon pairs using two micro-structured fibres,” New J. Phys. 9(8), 276 (2007).
[Crossref]

Azaña, J.

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546(7660), 622–626 (2017).
[Crossref] [PubMed]

Barbieri, M.

P. C. Humphreys, B. J. Metcalf, J. B. Spring, M. Moore, X. M. Jin, M. Barbieri, W. S. Kolthammer, and I. A. Walmsley, “Linear Optical Quantum Computing in a Single Spatial Mode,” Phys. Rev. Lett. 111(15), 150501 (2013).
[Crossref] [PubMed]

Belabas-Plougonven, N.

Bentivegna, M.

Bonneau, D.

G. J. Mendoza, R. Santagati, J. Munns, E. Hemsley, M. Piekarek, E. Martin-Lopez, G. D. Marshall, D. Bonneau, M. G. Thompson, and J. L. O’Brien, “Active temporal and spatial multiplexing of photons,” Optica 3(2), 127–132 (2016).
[Crossref]

J. W. Silverstone, R. Santagati, D. Bonneau, M. J. Strain, M. Sorel, J. L. O’Brien, and M. G. Thompson, “Qubit entanglement between ring-resonator photon-pair sources on a silicon chip,” Nat. Commun. 6(1), 7948 (2015).
[Crossref] [PubMed]

J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, V. Zwiller, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,” Nat. Photonics 8(2), 104–108 (2014).
[Crossref]

Brendel, J.

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Violation of bell inequalities by photons more than 10 km apart,” Phys. Rev. Lett. 81(17), 3563–3566 (1998).
[Crossref]

Briegel, H. J.

H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, “Quantum repeaters: The role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81(26), 5932–5935 (1998).
[Crossref]

Bromberg, Y.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351(6278), 1176–1180 (2016).
[Crossref] [PubMed]

Caspani, L.

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546(7660), 622–626 (2017).
[Crossref] [PubMed]

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351(6278), 1176–1180 (2016).
[Crossref] [PubMed]

Cassan, É.

Chae, C. J.

C. Xiong, X. Zhang, Z. Liu, M. J. Collins, A. Mahendra, L. G. Helt, M. J. Steel, D. Y. Choi, C. J. Chae, P. H. W. Leong, and B. J. Eggleton, “Active temporal multiplexing of indistinguishable heralded single photons,” Nat. Commun. 7, 10853 (2016).
[Crossref] [PubMed]

X. Zhang, I. Jizan, J. He, A. S. Clark, D. Y. Choi, C. J. Chae, B. J. Eggleton, and C. Xiong, “Enhancing the heralded single-photon rate from a silicon nanowire by time and wavelength division multiplexing pump pulses,” Opt. Lett. 40(11), 2489–2492 (2015).
[Crossref] [PubMed]

Chen, Y. A.

Z. Zhao, T. Yang, Y. A. Chen, A. N. Zhang, M. Zukowski, and J. W. Pan, “Experimental violation of local realism by four-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 91(18), 180401 (2003).
[Crossref] [PubMed]

Choi, D. Y.

C. Xiong, X. Zhang, Z. Liu, M. J. Collins, A. Mahendra, L. G. Helt, M. J. Steel, D. Y. Choi, C. J. Chae, P. H. W. Leong, and B. J. Eggleton, “Active temporal multiplexing of indistinguishable heralded single photons,” Nat. Commun. 7, 10853 (2016).
[Crossref] [PubMed]

X. Zhang, I. Jizan, J. He, A. S. Clark, D. Y. Choi, C. J. Chae, B. J. Eggleton, and C. Xiong, “Enhancing the heralded single-photon rate from a silicon nanowire by time and wavelength division multiplexing pump pulses,” Opt. Lett. 40(11), 2489–2492 (2015).
[Crossref] [PubMed]

Chu, S. T.

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546(7660), 622–626 (2017).
[Crossref] [PubMed]

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351(6278), 1176–1180 (2016).
[Crossref] [PubMed]

Cino, A.

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546(7660), 622–626 (2017).
[Crossref] [PubMed]

Cirac, J. I.

H. J. Briegel, W. Dur, J. I. Cirac, and P. Zoller, “Quantum repeaters: The role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81(26), 5932–5935 (1998).
[Crossref]

Clark, A. S.

Collins, M. J.

C. Xiong, X. Zhang, Z. Liu, M. J. Collins, A. Mahendra, L. G. Helt, M. J. Steel, D. Y. Choi, C. J. Chae, P. H. W. Leong, and B. J. Eggleton, “Active temporal multiplexing of indistinguishable heralded single photons,” Nat. Commun. 7, 10853 (2016).
[Crossref] [PubMed]

Cortés, L. R.

M. Kues, C. Reimer, P. Roztocki, L. R. Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546(7660), 622–626 (2017).
[Crossref] [PubMed]

de Riedmatten, H.

I. Marcikic, H. de Riedmatten, W. Tittel, H. Zbinden, M. Legré, and N. Gisin, “Distribution of time-bin entangled qubits over 50 km of optical fiber,” Phys. Rev. Lett. 93(18), 180502 (2004).
[Crossref] [PubMed]

Deutsch, D.

D. Deutsch, “Quantum-Theory, the Church-Turing Principle and the Universal Quantum Computer,” Proc. R. Soc. A Math. Phys. Eng. Sci.400, 97–117 (1985).
[Crossref]

Ding, D. S.

Y. H. Li, Z. Y. Zhou, L. T. Feng, W. T. Fang, S. L. Liu, S. K. Liu, K. Wang, X. F. Ren, D. S. Ding, L. X. Xu, and B. S. Shi, “On-Chip Multiplexed Multiple Entanglement Sources in a Single Silicon Nanowire,” Phys. Rev. Appl. 7(6), 064005 (2017).
[Crossref]

Z. Y. Zhou, S. L. Liu, Y. Li, D. S. Ding, W. Zhang, S. Shi, M. X. Dong, B. S. Shi, and G. C. Guo, “Orbital Angular Momentum-Entanglement Frequency Transducer,” Phys. Rev. Lett. 117(10), 103601 (2016).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1 The principle diagram for entanglement source. Multiplexed pulses pump an SNW to generate entangled photon pairs in N time slots. The entangled photon pairs are firstly split into temporal channels using a time division multiplexer (TDM), which is consist of optical switches. Then, the entangled photon pairs are distributed to multiusers by DWDM.
Fig. 2
Fig. 2 Experimental setup for multiplexed time-bin entanglement source. TA, tunable attenuator; PC, fiber polarization controller; UMI, unbalanced Michelson fiber interferometer; DDG1, DDG2, digital delay generator; FRM, Faraday rotation mirror; SSPD1 and SSPD2, superconducting single-photon detector; TIA, time interval analyzer. ODL, optical delay line.
Fig. 3
Fig. 3 Quality characterizations of time-and wavelength-division multiplexed entanglement source. (a). Raw visibilities of two-photon interference for 3 × 5 channel pairs. (b). Two-photon coincidence in 60s for channel S8-I8-T1 when the idler and the pump UMI phase is fixed at π/2 (solid blue line) and the idler and the signal UMI phases are fixed at π/2 (solid blue line) in channel. (c). Two-photon coincidence in 300s for channel S8-I8-T2 when the idler and the pump UMI phases are fixed at 0 (solid blue line) and the idler and the signal UMI phases are fixed at 0 (solid blue line). (d). Two-photon coincidence in 300s for channel S8-I8-T3 when the idler and the pump UMI phases are fixed at π/2 (solid blue line) and the idler and the signal UMI phases are fixed at π/2(solid blue line).
Fig. 4
Fig. 4 Experimental setup for HOM interference between photon pairs at different time slots generated from the same SSW. TA, tunable attenuator; PC, fiber polarization controller; DDG1, DDG2, digital delay generator; SSPD1 and SSPD2, superconducting single-photon detector; TIA, time interval analyzer; OC, optical coupler. ODL, optical delay line. TODL, tunable optical delay line.
Fig. 5
Fig. 5 Four-fold HOM interference fringes. (a). The measured four-fold dip between S14-I14-T3 and S14-I14-T2 channel pairs. (b). The measured four-fold dip between S8-I8-T1 and S8-I8-T2 channel pairs.
Fig. 6
Fig. 6 More data about the photon source. (a). single count rate for correlated channel pairs. (b). CARs for different correlated channel pairs from S14-I14-T1 to S2-I2-T3.

Tables (1)

Tables Icon

Table 1 Definition of the wavelengths of the standard ITU grids for the signal and idler photons

Equations (9)

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| ψ p 1 = 1 2 ( | S e i ϕ p 1 | L )
| ψ p 2 = 1 2 ( | S e i ϕ p 2 | L )
| ψ p 3 = 1 2 ( | S e i ϕ p 3 | L )
| Φ T 1 = 1 2 ( | S S e i 2 ϕ P 1 | L L )
| Φ T 2 = 1 2 ( | S S e i 2 ϕ P 2 | L L )
| Φ T 3 = 1 2 ( | S S e i 2 ϕ P 3 | L L )
V 1 1 + 8 μ 1 + 12 μ
C 4 = R μ 2 η s 2 η i 2 / 2
V 2 = 1 + r 2 1 + r 2 / 2

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